A099857 Expansion of (1+3x+x^2)/(1-3x+x^2).

1, 6, 18, 48, 126, 330, 864, 2262, 5922, 15504, 40590, 106266, 278208, 728358, 1906866, 4992240, 13069854, 34217322, 89582112, 234529014, 614004930, 1607485776, 4208452398, 11017871418, 28845161856, 75517614150, 197707680594

Offset: 0

Author

Paul Barry, Oct 28 2004

Keywords

• easy
• nonn

Comments

Hankel transform is 1, -18, -36, 0, 0, 0, 0, 0, 0, 0, 0, ... - Philippe Deléham, Dec 15 2011

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..2391
• Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
• Index entries for linear recurrences with constant coefficients, signature (3, -1).

Crossrefs

Cf. A000045, A099856, A099858.

Programs

Mathematica

CoefficientList[Series[(1+3x+x^2)/(1-3x+x^2),{x,0,30}],x] (* Harvey P. Dale, May 23 2015 *)

Formula

a(n) = 0^n + 6*Fibonacci(2*n).